The injury ruled the 20-year-old out of Tottenham's 1-1 draw at Arsenal in the Premier League on Sunday.
Pochettino blasts Spurs after 'embarrassing' defeat against Leverkusen
The injury means Alli will also miss the World Cup qualifier against Scotland and friendly with Spain.
"Bad luck, yesterday in the training session, he twisted his knee. We need to assess him today and tomorrow," Pochettino said, in comments published on Tottenham's Twitter account before the game.
"He'll be out for a few weeks. We hope it's not a big issue. It's bad luck. He was in the team, he's an important player, but that's football."
Relentless Cherries deny Spurs win
Speaking after the game, Pochettino said Alli's injury was "minor".
Signed from Milton Keynes Dons in 2015, Alli was voted the Professional Footballers' Association Young Player of the Year last season after Spurs finished third in the league.
Southgate was also left sweating on the fitness of first-choice right-back Kyle Walker, who hobbled off after taking a knock in the second half.
"I've not had time to see him yet," Pochettino said when asked about Walker's injury after the game. "He's with the doctor at the moment and we'll see after the press conference."
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ